THE MOUSAI TITANIDES were three or four elder Muses, the Titan goddesses of music. They were named Melete (Practise), Aiode (Song), and Mneme (Memory). The last of these was surely identified with the Titanis Mnemosyne (also Memory), mother of the nine celebrated Olympian Muses by Zeus.

The two sets of Muses, however, were really just alternate versions of the same set of goddesses. A third group were the Muses Apollonides.

Alcman, Fragment 67 (from Diodorus Siculus 4. 7. 1) :
"Most of the mythographers, including those of the highest reputation say that he Mousai are the daughters of Zeus and Mnemosyne; but one or two of the poets, Alkman among them, make them the daughters of Ouranos (Sky) and Ge (Earth)."

Diodorus Siculus, Library of History 4. 7. 1 (trans. Oldfather) (Greek historian C1st B.C.) :
"As for the Mousai . . . the majority of the writers of myths and those who enjoy the greatest reputation say that they were daughters of Zeus and Mnemosyne (Memory); but a few poets, among whose number is Alkman [lyric poet C7th B.C.] state that they were daughters of Ouranos (Sky) and Ge (Earth). Writers similarly disagree also concerning the number of the Mousai; for some say they are but thee, and others that they are nine, but the number nine has prevailed since it rests upon the authority of the most distinguished men, such as Homer and Hesiod and others like them."

Pausanias, Description of Greece 9. 29. 1 (trans. Jones) (Greek travelogue C2nd A.D.) :
"The first to sacrifice on Helikon to the Mousai and to call the mountain sacred to the Mousai were, they say, Ephialtes and Otos, who also founded Askra. To this also Hegesinus alludes in his poem Atthis [Greek poet uncertain date] . . . This poem of Hegesinos I have not read, for it was no longer extant when I was born. But Kallipos of Korinthos [Greek writer C5th B.C.] in his History of Orkhomenos uses the verses of Hegesinos as evidence in support of his own views, and I too have done likewise, using the quotation of Kallipos himself . . .
The sons of Aloeus [the Aloadai] held that the Mousai were three in number, and gave them the names of Melete (Practice), Mneme (Memory) and Aoede (Song).
But they say that afterwards Pieros, a Makedonian, after whom the mountain in Makedonia was named, came to Thespiai and established nine Mousai, changing their names to the present ones . . .
Mimnermos [Greek poet C6th B.C.], who composed elegiac verses about the battle between the Smyrnaians and the Lydians under Gyges, says in the preface that the elder Mousai are daughters of Ouranos (Sky), and that there are other and younger Mousai, children of Zeus."

Cicero, De Natura Deorum 3. 21 (trans. Rackham) (Roman rhetorician C1st B.C.) :
"Again the first set of Musae are four, the daughters of the second Jupiter [i.e. Ouranos], Thelixonoe, Aode, Arche and Melete. The second set are the offspring of the third Jupiter [i.e. Zeus] and Mnemosyne, nine in number."

Arnobius, Against the Heathen 3. 37 (Roman Christian rhetorician C3rd A.D.) :
"We are told by Mnaseas [Greek writer C3rd B.C.] that the Muses are the daughters of Tellus [Gaia the Earth] and Coelus [Ouranos, Heaven]; others declare that they are Jove's by his wife Moneta [Mnemosyne, Memory], or Mens (Mind) [Metis?]; some relate that they were virgins, others that they were matrons. For now we wish to touch briefly on the points where you are shown, from the difference of your opinions, to make different statements about the same thing. Ephorus [historian C4th BC], then, says that they are three in number; Mnaseas, whom we mentioned, that they are four ; Myrtilus brings forward seven; Crates [the philosopher? C4th B.C.] asserts that there are eight; finally Hesiod, enriching heaven and the stars with gods, comes forward with nine names."